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I Don't Believe in Imaginary Property writes "On February 5, 1897, 111 years ago today, the Indiana legislature very nearly passed a bill 'introducing a new mathematical truth,' that would have erroneously established pi as the ratio 'five-fourths to four' or 3.2. The story explaining the rationale behind the bill and how they were prevented from legislating it when a real mathematician intervened is quite interesting, because the man who discovered the 'new mathematical truth' wanted to charge royalties, which could have made pi the first form of irrationalproperty."

thats because pi to 4 decimals is 666/212 so therefore anything close real pi is of course the devils work. (I can't believe I just stumbled on something more accurate than 22/7 by accident while trying to make a real lame joke)

Then again, maybe I'll patent 22/7 as a good way to approximate pi. I heard that intellectual property is all the rage nowadays.

Hm... no, you need a process. Those are what all the cool corporations do. Patent the process of "dividing two, common whole numbers for the purpose of usefully approximating the ratio between the diameter and the circumference of a circle". Then make sure the steps described take up at least three pages. Oh and use a lot of impressive sounding words for things. Never say something like "pencil", say "graphite based, portable diagrammatic device rated at two on the graphite integrity scale". Things like that. The USPTO seems really impressed when they haven't the slightest idea what you're talking about.

Hmmm... when I was young, I was taught that the diameter of a (bounded) set S in a metric space was the maximum (well, supremum) of the distances between any two elements in S. Seem a much simpler definition to me.(And wikipedia mentions this one, too)

The Hebrew alphabet is alphanumeric: each Hebrew letter also has a numerical value and can be used as a number.

There was an embedded code - a word that was written strangely:

The common word for circumference is qav. Here, however, the spelling of the word for circumference, qaveh, adds a heh (h)....
This indicates an adjustment of the ratio 111/ 106, or 31.41509433962 cubits. Assuming that a cubit was 1.5 ft. this 15-foot-wide bowl would have had a circumference of 47.12388980385 feet.
This Hebrew "code" results in 47.12264150943 feet, or an error of less than 15 thousandths of an inch!

Numerology wins you no points. If you translate "No God" by a=1, b=2 etc then you get the string of numbers 14157154, which is actually found in pi at the about the 142 thousandth digit. What does this mean? Nothing.

The q has a value of 100; the v has a value of 6; thus, the normal spelling would yield a numerical value of 106. The addition of the h, with a value of 5, increases the numerical value to 111.

Hebrew letters have associated numerical values, that's well known. For the purposes of the argument I'll accept that these letters have the cited values.

But exactly how did they come up with this particular formula? Given three numbers [A,B,C] what methodology tells them to interpret the combination as the ratio (A+B)/(A+B+C) and not, say, A+B+C or A+B*C, or (A+B)/(A+C)? I don't think there is such a methodology, and I think this means that they will pick whatever formula works for the occasion.

Mathematician: Pi is the ratio of the circumference of a circle to its diameter.Engineer: Pi is about 22/7.Physicist: Pi is 3.14159 plus or minus 0.000005Computer Programmer: Pi is 3.141592653589 in double precision.

Does any idiotic thing get modded up as long as it blasts Christianity? Nowhere in the Bible does it talk about the principles of Euclidian geometry.

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." -- First Kings, chapter 7, verses 23 and 26

Which doesn't say that pi = 3 any more than saying "And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty-one and four-tenths cubits did compass it round about....And it was an hand breadth thick...." says that pi = 3.14.
Pi is, in fact, equal to neither of those numbers, nor to 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510.
It is an irrational number for which any representation in digits is an approximation. And 3 is the proper approximation of pi to one significant digit.

Unfortunately the Egyptians had calculated it as 4 * (8/9)**2 in about 1650BC (Rhind Papyrus), this comes to about 3.16. Archimedes (287-212 BC) estimated it to lie between 223/71 and 22/7. The Chinese and Indians had also got reasonable estimates at about the same period.

Just goes to show you can't believe everything put forward by a set of bronze/iron age goat herders.

But there are people [mikehuckabee.com] who say that every word of the bible is literal truth. You've just attempted to claim that the bible approximated something - in other words, that it's not 100% true.

Normally we'd just ignore those people, and agree that the bible rounded something for brevity. But when those people represent a significant proportion of the voting public (fortunately, splitting their vote between two candidates), it's worth pointing out that they exist and would have burned you at the stake 300 years

Doesn't anyone know math or science? In scientific notation, you count the significant digits. All of the numbers have one (1) significant digit. It's amazing God got it right thousands of years before science was invented. Go figure.

They are not working with double digits. They are using single digits: 10 cubits... 30 cubits...
In scientific notation, you count the significant digits. All of the numbers have one (1) significant digit

Not quite. "10 cubits" and "30 cubits" might be to either one or two significant figures; since it doesn't specify, there no way of telling which. If they had they been given in scientific notation, as either, e.g., "3*10^1" or "3.0*10^1", then you're right, that would have been one and two s.f. respectively; but "30 cubits" is ambiguous.

The problem is that it's the same logic and methodology that lets fundamentalist Christians abuse gays and reject evolution. Take a portion of the Bible literally, throw out anything that contradicts it (for these purposes), and raise a stink.

The Bible clearly shows the ratio of the circumference of a circle to its diameter is 3. Your talk of significant digits is just trying to draw worship away from God.

roundadj1 shaped like, or approximately like, a circle or ball. 2 not angular, with a curved outline (Chambers 21st Century Dictionary)

So, according to definition 2, an ellipse is round, for example. And depending on the eccenticity, the ratio of circumference to diameter (major axis) of an ellipse can be anywhere between 2 and pi: 3, maybe?

Or fourth option: we're misinterpreting the text, helped along by reading our desired conclusion into it. Apparently another quote concerning the same object mentions that it had a flared rim "like a lily". So if you measure the diameter of the flared rim, but the circumference of the (narrower) cylindrical portion of the sides, you're definitely not going to end up with a good approximation of pi.
Personally I think there are much more valid reasons for criticising the scientific validity & alleged inerrancy of the Bible than that little gem. It really takes effort to read that quote as a statement that pi = 3.0.
There are other less credible justifications: eg, that the cubit was not a well defined unit (doubtful in my mind, you wouldn't be able to do very good architecture or even carpentry without a measurement unit consistent from one dimension of an object to another). And even utterly specious arguments hinging on numerological rubbish.

The fifth option is far more likely: Accurately measuring and recording the circumference wasn't that important to them, so they either didn't measure it well, or else they rounded it off. The diameter probably wasn't exactly 10 cubits, either.

1 Kings 7:23 "He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it." or "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about."

While the Bible doesn't actually state the nature of pi, and a cubit is an extremely rough unit anyway, it's amusing to note that if you properly define cubit as being a fixed length and assert that the word circular refers to a near-perfect circle, the units just don't work out unless you redefine space, and along with it, Pi. Putting the "fun" back in "fundies".

a) the measurements are not rounded.This seems quite unlikely for a start. Should the author have written "He made the Sea... measuring nine point five five cubits from rim to rim..."?

b) the Sea was a plain cylinder.Another possibility, not ruled out by the text, and certainly well within the realms of probability is that the rim had a lip or a flare to it. So the distance from rim to rim would be greater than the distance across the circumference measured lower down by the line. (Think about the practical difficulty of measuring with a line around the outside of a flared rim.)

In fact it doesn't matter which of the above two explanations is more likely, since no one (apart from those trying to point out inconsistencies in the Bible) is asserting that the story quoted says anything at all about the accurate value for pi.

There's also "precedent" for the OT's use of significant digits or rounding. Though the upper bound of human lifespan is stated at 120 years (either a Really Good Guess as to what would apply over the next few thousand years, and several billion future people, by a nomad who probably knew a couple hundred people personally--or divinely inspired, depending on your predisposition), and we have evidence that (at last check of Guinness) a couple recent people lived to 122.So, 31.415926535 as 30, 122.x as 120 w

Introduced by Record
IN THE SENATE
Read first time and referred to
committee on Temperance, February 11th, 1897
Reported favorable February 12th, 1897
Read second time and indefinitely postponed February 12, 1897

There was an attempt to outlaw i and it's use in mathematical equations. Lawmakers who objected to its use complained that it wasn't real and their constituents required too much imagination to accept it.

There was an attempt to outlaw i and it's use in mathematical equations. Lawmakers who objected to its use complained that it wasn't real and their constituents required too much imagination to accept it.

What's really sad is I don't know if that's a joke or if it's informative.

I mean, and I'm 100% serious here... It could go either way. I have no clue!

if we're making bad puns, don't forget the story of Polly Nomial and Curly Pi

Once upon a time pretty little Polly Nomial was strolling across a field of vectors when she came to the edge of a singularly large matrix.

Now Polly was convergent and her mother had made it an absolute condition that she must never enter such an array without her brackets on. Poll however, who had changed her variables that morning and was feeling particularly badly behaved, ignored these conditions on the ground that they were unnecessary, and made her way amongst the complex elements.

Rows and columns enveloped her on both sides. Tangents approached her surface; she became tensor and tensor. Quite suddenly two branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense of directrix and went completely divergent. As she reached a turning point she tripped over a square root which was protruding from the erf and plunged headlong down a steep gradient. When she was differentiated once more she found herself alone, apparently in a non-Euclidian space.

She was being watched however. That smooth operator, Curly Pi, was lurking inner product. As his eyes devoured her curvilinear co-ordinates, a singular expression crossed his face. Was she still convergent, he wondered. He decided to integrate at once.

Hearing a vulgar fraction behind her, Polly turned round and saw Curly Pi approaching with his power series extrapolated. She could see at once by his degenerate conic and his dissipative terms that he was bent on no good.

"Eureka" she gasped.

"Ho Ho" he said, "what a symmetric little polynomial you are. I can see you're absolutely bubbling over with secs."

"Come, come," said Curly, "lets off to a decimal place I know and I'll take you to the limit".

"Never" gasped Polly.

"EXCHLF" he swore, using the vilest oath he knew. His patience was gone. Coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He started at her significant places and began smoothing her points of inflection. Poor Polly, all was up. She felt his digit tending to her asymptotic limit. Her convergence was gone for ever.

There was no mercy, for Curly was a Heavyside operator. He integrated by partial fractions. The complex beast even went all the way round and did a contour integration. What an indignity. To be multiply connected at her first integration. Curly went on operating until he was absolutely and completely orthogonal.

When Polly got home that evening her mother noticed that she was truncated in several places. But it was too late to differentiate now. As the months went by, Polly increased monotonically. Finally, she generated a small but pathological function which left surds all over the place until she was driven to distraction.

The moral of the story is this: If you want to keep your expressions convergent, never allow them a single degree of freedom.

Concerned readers of the rather lurid tale above may rest assured that its scandalous contents are entirely false.

Mr. Pi is a well known and well respected number in the mathematical community, who despite its irrational tendencies, has won the hearts of all decent magnitudes with its transcendental nature. A nature one might add, which intrinsically prevents it from appearing at the roots of any finite order equation, let alone one of only seventeenth order.

Mr. Pi is a good friend to many highly respected mathematical families such as the Trigonometric Functions and the Elliptic Functions. It is also known for its generous community work, appearing in many Geometrical texts and Physics equations, and in general is known far and wide for not holding itself above the common constant, despite its fame and status.

Mr. Pi has been known for years as a wonderful role model and teacher for polynomials of a small degree, particularly for second order equations. It has opened up worlds of possibility and inspired these young equations for many years, and it would be a great shame if this false, cruel and libelous fiction caused an end to those efforts.

I urge readers to reject and condemn this utterly false, malicious and libelous insult upon a good member of the mathematical community. We must not abandon the rigor and scruple that our community is renowned for, and succumb to emotive reasoning. The reader may be assured that however rational their coefficients, seventeenth order equations are known to come across irrational roots, of any multiplicity, all by themselves!

Kind of like the attempt in Kansas to declare the use of the "term one million years BC" as a religious hate crime since it shows religious intolerance. Like the "N" word the "M" word was very hurtful to the faithful given there was no one million years BC and there can't be a one million years AD since the Rapture is around the corner. When asked about one billion years the response was "now you're just being silly."

I'm sure every sane engineer would look at that 3.2 and decide that, for reasons related to what's practical and works well, the exact 3.20000000 can't be used with full precision, instead a rough approximation is needed, say 3.14159265 or thereabouts.

I'm sure every sane engineer would look at that 3.2 and decide that, for reasons related to what's practical and works well, the exact 3.20000000 can't be used with full precision, instead a rough approximation is needed, say 3.14159265 or thereabouts.

... and not too long ago, there was an article about engineers supposedly having a terrorist mindset. I think we could add "Criminally adulterating the legislated value of pi" to the list of possible terrorist acts.

And do you know what the really scary part is? I had an engineering buddy back in undergrad (at the University of Michigan, not exactly a terrible engin school) vociferously argue with me that pi was exactly 22/7. I asked him if he know what an irrational number is--he said yes. I asked him if he accepted that pi is an irrational number--he said yes. I asked him how pi could be exactly 22/7 if it is irrational... What an exhausting conversation that was. It turns out that pi wasn't the only irrational part of that conversation.

"It is impossible to compute the area of a circle on the diameter as the linear unit without trespassing upon the area outside of the circle to the extent of including one-fifth more area than is contained within the circle's circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight."

As a Hoosier (DEF: born and currently a resident of Indiana), I confidently assure you that they would gleefully pass the bill today. Anyone objecting would be branded a pi-denier. [insert boring local politics]

No politician wants to be the one refusing to give our poor and homeless their much needed pi.

They would have been behind their time literally, at least when they tried to make a pendulum clock! using T=2 *Pi * Sqrt(l/g) they would have produced a pendulum which was too long and therefore slow.

Apparently, the bill's main purpose wasn't to establish a value of Pi, but to provide a method to square the circle [wikipedia.org]. Doubly retarded! Also, why do we need LEGISLATION of squaring the circle? What political significance does this hold, other than the fact that politicians can't math?

I hope we read this in about 100 years....
About 100 years ago, the Dover Pennsylvania school board very nearly succeeded in enforcing 'introducing a new scientific truth,' that would have erroneously established intelligent design as a rational alternative to evolution. The story explaining the rationale behind the idiocy is best described by the federal judge who prevented the school board from....

And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man's ability to comprehend.

This, along with the rest of the math in the bill, makes it clear that the authors were the sort that only "believe" in rational numbers. Of course, by that time mathematicians already had a pretty good hold on the rest of the real numbers, and there wasn't any mystery at all about the existence of numbers that weren't the ration of two integers. The only real mystery here is why they preferred the approximation 3.2 rather than 3.1. Not that either is good enough for engineers, who routinely used 3 places as the minimal precision if you don't want to be laughed out of the room.

One of my favorite bits of mathematical humor is the many cases where they have taken criticisms and turned them into terminology. Thus, when it was realized that numbers like e and pi couldn't be written as ratios of integers, there were a lot of dummies who didn't accept this, and attacked the rationality of the people who did. The response of mathematicians was to say, in essence, "Hey, they call us irrational; that's a good word. Let's call the numbers that our critics believe in as 'rational', and the numbers that they don't believe in as 'irrational'. They'll be happy, and we'll have handy words for talking about these two kinds of numbers."

It happened again when people started talking about square roots of negative numbers (and engineers found practical uses for them in the real world). There were the usual criticisms, to the effect that negative numbers don't have square roots, and it's stupid to talk about things that don't exist. The natural (;-) reaction of the mathematicians was to first be bemused by the very idea that any kind of numbers have any sort of real existence. Then they adopted the critics' words as terminology, with 'real' numbers the sort that the critics accepted, and 'imaginary' numbers the kind that produced negative numbers when multiplied by themselves. That must have really played with the critics' minds. "Oh, you want to talk about real numbers; that's room 12A, just along the corridor. We're talking about imaginary numbers here. Stupid git."

Of course, there's the even more basic concept of 'natural' numbers, i.e., positive integers. It's clear from most most languages' words for numbers that most people historically have only dealt with this sort of number. Even today, many US high-school kids have a certain resistance to the idea that they have to learn about fractions, which strike them as 'unnatural' and pointless. So mathematicians adopted 'natural' as a subtle jab at the irrational attitude of the ignorant masses.

At least this bill's authors had enough understanding to accept rational numbers as real, though they classified irrational numbers like pi as "insolvable mysteries". It is sad (and funny) that as late as 1897 this sort of ignorance could actually make an appearance in a legislative body and apparently be taken as anything but a lame joke.

There have been other bills like this in the past, though as far as I've read, none of them has ever actually been passed, or even voted on. Anyone know of a case where one reached a vote?

I don't mind giving ownership of Pi to some clever patent lawyer. But no sneaking using a mathematical symbol. We need to know the EXACT value they want to patent. So they would first have to write down ALL the digits before I would be willing to hand over the patent.
In fact, I propose that we begin this process right now. Something as widely used as Pi is sure to bring in billions. We need to get ALL the lawyers busy writing down the digits of Pi immediately.

Well, we do try. I'm working on legislating e^(i*pi)+1 to equal not zero, but a kajillion billion. You see, by taking the quadrangent of pi (valued at exactly 3) and the linear arc of the glayben, we obviously get a far superior answer than the old, wanting, junky answer that Euler crapped out most likely on ye olde toilet. And, best of all, you too can use the Toilet-Free Euler Identity (T-FI) for the low price of 9.95 US dollars... in your own home! Deals like this don't last forever, folks, but if you hi

are all circumference/diameter(on the surface) ratios rational? If not, how many are not?

As the circle expands from a point to a great circle, the ratio between circumference and diameter can take any value between pi and two. So an infinite number of possible ratios are rational, and in infinite number are irrational.

Interestingly, however, if you pick a particular circle, the ratio actually has a 100% probability of being irrational, rather than rational. Informally, this is because the irrationals are so much 'denser' than the rationals (using the colloquial rather than the topological meaning of dense). A proper proof follows from the fact that the rationals have Lebesgue measure 0; i.e. they can all be enclosed in a set of intervals on the real line, the sum of the lengths of which can be made as small as you like.

It's also a well-known bit of historical legislative foolishness often cited to demonstrate the kind of bad decisions possible in a representative system of government. In an election year, it's a valuable reminder of how we need to keep a close eye on these people.

Considering the repeated movements to introduce other bits of absurdity into school curricula (ID, anyone?) it's well worth talking about.